The story is undeniably insane. In 1980, three 19-year-old men looking exactly alike met by happenstance, learning that they are identical triplets separated at birth.

Bobby, Eddy and David made national headlines for their unbelievable story, all the while getting to know each other for the first time. Aside from looking exactly alike, they share uncanny similarities.

They were all high school wrestlers. They all smoke Marlboro cigarettes. They have the same taste in women, and they finish each other’s sentences like they’ve known each other their whole lives. Their similarities are all the more striking considering that they were all adopted to very different households: blue collar, middle class and wealthy.

As the warm glow of their reunion fades, the triplets start asking questions. Namely: Why were they separated? Why didn’t they know of each other’s existence?

The answers will prove outrageous and disturbing, changing each of the triplets’ lives in ways they never could have expected.

I’ll leave it at that because Tim Wardle’s new documentary, “Three Identical Strangers,” has more twists and turns than an airport potboiler. The movie plays like a thriller, perhaps even to a fault.

Wardle’s style is a little overcooked. His strategy is to withhold information until later in the film, the bombshells starting to drop in the last 40 minutes. The revelations have the feel of a soap-opera cliffhanger playing ahead of a commercial break.

This can prove as enervating as it does exciting. Because in “Three Identical Strangers” the jaw-droppers are typically jaw-droppers only because the filmmakers decided to elide essential parts of the story until closer to the end.

This can be brutally effective. Especially when the film starts to unravel the mystery of the triplets’ history.

But it can just as often feel clumsily manipulative. The film, for instance, will take an earlier moment or interview clip and repeat it, sometimes multiple times, reminding you of some important piece of information before unveiling some new wowza! But by the time the bombshell drops, astute viewers will have already guessed what’s going on.

Such narrative sleight-of-hand can be a good way to tell a story, but it has to feel organic. With “Three Identical Strangers,” Wardle doesn’t seem to trust the material enough to tell the story straight. And that’s too bad, because it’s one hell of a story.

But if the film’s overall structure is a bit of a bungle, its form, at least, isn’t lacking.

Wardle mixes extensive archive footage with new interviews with the brothers. Some of the story calls for reenactments, and these scenes play like the cinematic interludes of an Errol Morris doc: crisp, artful, paranoid.

Eventually, Pulitzer Prize-winning journalist Lawrence Wright (“Going Clear,” “The Looming Tower”) enters the picture. Wright investigated the triplets’ troubling origins in the ’90s, and his reporting turned up more than a few disquieting details.

The film dovetails the past and present lives of the triplets with some fairly stimulating stuff. And “Three Identical Strangers” zooms out to look at a much bigger picture.

In the end, this isn’t the feel-good movie it at first appears to be, but something far more disorienting — a film that leaves the viewer with lingering questions about identity, human nature and free will.

In the end, this was far too extraordinary a story to be spoiled by a little wonky storytelling.

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